Approximative methods in the semiclassical theory of multiphoton processes

The present work aims at giving a theoretical background for the several theoretical methods existing in the literature describing multiphoton processes. Within the framework of the semiclassical theory a general expression for the multiphoton transition probability is given — using the formal time-dependent theory of scattering and the general properties of the Schrödinger equation of the problem. The amplitude of the multiphoton transition is a generalisation of the stationary transition operator for the non-stationary case. Using the general expression of the transition probability we compare the different non-perturbative approaches with the perturbation theory and establish the limits of their applicability.